Year 8 Wrap-Up

Another year of teaching wrapped up last week. It was a bit of a roller coaster of a second semester in terms of both my personal and professional life, but I made it through. The end of the year was its typical insanity, plus a bit tougher than usual since almost my entire scholar bowl team graduated. As I transition to prepping for next year, here are a few goals.

Things to keep doing:

• Kids really like my warm-ups and they were mentioned on multiple course evals — maybe change ACT prep to “How Many?“
• FlipGrid — but be more consistent second semester, and use in Alg. 2 (instead of Calc?)
• I added reflection questions to my assessments in Alg. 2, which I liked and want to add to the rest of my classes

Things to improve:

• Deeper tasks/assessments — take home quizzes?
• More breaks mid-lesson for discussion
• Mini-conferences — I did these once and then forgot about them
• More celebrations of the positive

Things to stop:

• Phone distractions — some kids use them as calculators, but there was a lot of creep on distractions later in the year, so I think I need to go back to requiring them to be out of sight
• Problem of the Week? — Not many kids have one it the past couple of years, so maybe I need to come up with something else

In other news, I’m teaching a non-math class for the first time, which will be an adventure and is also slightly terrifying. I’m teaching a fundamentals of education course for students who might be interested in the education field. So that will be my main summer project. Looking at the topics (history of ed, legal issues, etc.) reminded me that I didn’t love this course in college, so I’m going to have to see what I can come up with to make it less dry.

Solids of Revolution Volume Project

One of our last topics in Calculus is volume of solids of revolution. I teach disc method first, then shell method. Between the two, we were desperately in need of something to mix up too many days of direct instruction and practice problems, so I wrote up this project during parent-teacher conferences.

Project HandoutDownload

Essentially:

• Find an object with a circular cross-section
• Measure it, photograph it, insert into Desmos and write functions to model its outline
• Write and calculate the necessary integrals for the solid of revolution
• Summarize your work in some format and compare your volume to the true volume of the object if possible

Lessons learned:

• Photograph objects carefully so that nothing is skewed
• MEASURE CAREFULLY! and then MEASURE AGAIN!!!
• Be sure to CENTER the object on the axis in Desmos!
• I’m okay with students using Wolfram Alpha for the integral calculations because by hand takes FOREVER with those equations from regression models.
• Remind students what a piecewise function should look like.
• Have a measuring cup/beaker handy to measure the true volume.

Overall, I thought this was a pretty cool project, although a few of my students had some error due to issues listed above. One student got within ONE ml of the true volume though, which was pretty amazing!

Graph Art 2019

My Algebra 2 Students did an awesome job on their project! Click on the title to see their equations and full graph.

Cat

Trent

Pusheen

Grace

Taj Mahal

Madeline

Airplane

Joseph

Dog

Tanner

Chiefs Logo

Coltin

Vince Vaughn

Matthew

Dog

Sadie

Grim Reaper

Cole

Turkey

Landon

Llama

Kaitlin

Seascape

Floyd

Converse Shoe

Jaiden

Landscape

Elliott

Car

Zyan

Cow

Alyssa

Blues Note

Noah

Guitar

Kylee

Rick

Caden

Pizza

Jazzlynn

Desmos Art Project (Update)

I’ve been having my Algebra 2 students create a piece of art using different functions and transformations for several years now. I’ve blogged about it in the past, but have changed several things along the way to make it go more smoothly. So here’s an update.

Directions & HandoutDownload

Day 1:

I hand out the directions and give students a minute to read through the first page. I ask then ask them to fill out the column describing the different shapes of the functions, and remind them that they can type and equation into Desmos if they’ve forgotten what something looks like. I check their tables, and then they work through a Desmos Activity that teaches them how to restrict domain and range, etc. Usually there is about 10 minutes left after they finish, and I get them logged into the Desmos app and they start deciding what art they want to make.

Days 2 – 3:

They work! I answer lots of questions and they submit a screenshot at the end of each hour so I can track their progress.

Day 4:

Ideally, students are close to wrapping up. I ask them to use their completed art to finish the rest of their tables, listing an example of each function type and describing one of each type of transformation. They save one last time and share email their link to me.

Things that have been a game changer:

Having students work through the intro activity on Desmos to practice their restrictions on domain and range before they leap in has helped a lot. Also the ability to log into the app and save vs. having to use the browser has led to less tech issues. Many students like the option to insert and image in the background of their graph and use it to guide their equations.

This is still my favorite project! My students always go above and beyond. I’ve taught them how to turn absolute value graphs sideways, turn circles into ellipses, and use trig function graphs. The directions only require 10 functions, by the average is around 50.

March is a Mess (and so am I)

*Disclaimer – this is kind of a ramble and has nothing to do with math content.*

I have been struggling big time recently. I don’t think I’m alone in this, but March seems like that’s when things fall apart for me every year. This March has been exceptionally difficult. I’m exhausted, feel like I have 500 things to do, and have been stressed about uncertainty in the upcoming year (finding a new coworker yet again, changing principals, etc.). My grandmother also passed away, making things especially hard.

About the only thing that has kept March bearable is that it’s the height of Scholar Bowl season, which I love coaching. I’m so thankful for my team (and their families) for being there for me this year. They got me flowers and candy, put up with my inability to keep track of any of my items at tournaments, and accept our sometimes unorthodox ways. This year almost my entire team is graduating, so it’s also breaking my heart a little.

My teaching hasn’t been the best this past month. I’ve scrapped some activities because I didn’t have the energy, haven’t participated in PD, and have been an emotional mess at times. Sometimes all we teachers seem post online is the good stuff. Then we look at the other amazing educators out there and think we should be doing more. No one is fantastic all the time. You are doing your best and that is enough.

The Unit Circle

We just wrapped up our intro to radian measure in Trig, which includes the unit circle. My personal philosophy is that students don’t really need to memorize the unit circle, because if you understand where it comes from, you can always derive it. I’ve done a “build the unit circle” activity for a few years, but I’ve never blogged about it, so here it it is.

Unit Circle Example and HandoutDownload

Basically students get a blank unit circle and bunch of 30-60-90º and 45-45-90º triangles with the hypotenuse labeled as one unit and then they have to find the rest of the side lengths and use them as measuring tools to figure out the coordinates of the points on the unit circle.

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At this point my students do have the two special triangles memorized, have thought about 60º = π/3 because it’s 1/3 of the way to 180º, and know that sin(ø) = y/r, etc. I don’t allow them to use calculators or really give them any help during this activity. They struggle a little bit a first, but they get there.

I like this activity because I think it helps students see the connection between the unit circle, coordinate definitions of the trig functions, and right triangle definitions of the trig functions. It’s also a nice hands on day to mix it up. I remember that making the handout so that the angles and triangles actually work in the circle was a pain, so I thought I’d share!

Snow Days

I haven’t blogged for a while because I hadn’t been to school in ages. We’re up to 20 snow days and I finally got to go back on Thursday and Friday of last week. We’re only required to make up 10 days and my seniors will only make up 5. That means I’m struggling when it comes to fitting in required topics by the end of the semester. Mostly this is an issue in Trig, with it being a one semester college-credit class (and I lost 20% of my instructional time). I’m doing my best to chill, but the forecast for next week doesn’t look great either.

Ways I’ve been coping…

• I’ve cut out almost every project, work day, several review days, and a few topics out of desperation
• I’ve been teaching during snow days via YouTube videos, email, and group chats
• Answering questions via FlipGrid boards
• I held “office hours” one afternoon when the weather was acceptable
• We’ve switched to take-home quizzes instead of in-class quizzes

But it’s been rough. Honestly, these kids aren’t going to get as good of an educational experience as if we hadn’t missed all this school. And I hope no one cares about standardized test scores, because we’re about three units behind in Algebra 2.

Things I’ve learned along the way:

• Tips for making a YouTube Video
  • Screen Record my written work in Notability (no microphone, because it doesn’t work anyway when you post)
  • Import into iMovie, increase speed to 1 1/2 to shorten, then voice-over
  • Upload to YouTube

• Good take-home quizzes are HARD to write
  • I made several versions, but told them they could use their notes, book, or work together (why only punish the honest kids?)
  • I don’t want students to just be able to Google or use Wolfram Alpha, so I’m doing a lot of “Tim found the value to be 1/2, explain what work he could have done,” or “describe and correct the mistake”
  • I gave students feedback and let them revise before giving a final score

My Calc class is the best and I found this bag on my porch on day when it was obvious I was feeling super stressed

Algebra 2 Polynomials Unit

I’ve never been a huge fan of the polynomials unit that I teach in Algebra 2. It’s some pretty abstract stuff at times — factors, zeros, degree, end behavior, and crazy graphs. I took a bit of time over the summer and Christmas break to redo it, and while there’s still room for improvement, it’s SO MUCH BETTER now.  Blogging so I can remember how things turned went.

Outline: (class notes I use with students here)

• Day 1: Lecture/notes on synthetic division, factoring higher degree polynomials, finding zeros. Debating moving this to between days 5 and 6.
• Day 2:  Intro to end behavior (Desmos Activity) – handout to fill in as we go along. If students struggled to notice the difference in end behavior was due to even/odd degree, making a table on the board with the degrees of the polynomials in the purple/orange group helped.
  
• Day 3:  Follow up to end behavior – lecture notes on notation, Kahoot!
• Day 4:  Polygraph Polynomial Graphs for about 20 minutes, paused and discussed increasing/decreasing, turning points, roots, and concavity. Followed-up with notes on those same concepts after playing.
  
• Day 5: Connecting graphs to equations (Desmos Activity). Students wrote equations to match given roots, and looked at how the factored form of a polynomial relates to its graph.  Discussed multiplicity and fundamental theorem of algebra.
  
• Day 6: Lecture notes on sketching graphs of polynomials — focused only on general shape and intercepts.
• Day 7: Solving polynomial equations by graphing (Desmos Activity).
  

I think incorporating all of the Desmos Activities I made (or borrowed) has helped us make much better connections between polynomial graphs and equations. Yay!

FlipGrid Semester Review Project

It’s almost the end of semester, thank goodness! We ended up without enough time to complete another unit in Algebra 2, so I assigned students a project to help review the semester’s content before their exam. Here is the handout/direction sheet I gave them.

There were two parts: making mini-review lessons/videos, and watching some of each others’ videos. We spent four days of class working on this project. Day 1 was spent planning, days 2 & 3 were spent recording videos, and day 4 was spent watching and replying.

To assign topics for part one, I made a list of all the sections we’d discussed this semester, printed off 2 copies and cut them up, and had students draw one topic from three different units. They then chose a fourth topic on their own. Students were asked to give an overview of the topic with several examples, a “try it” problem for viewers to do on their own, and an answer to the “try it” problem to check with. For part two, students chose four topics to watch videos on, worked out the “try it” problem, and left a reply explaining their solution.

Overall, I thought it went pretty well. Students did a good job on their topics for the most part, although they could improve their creativity a bit. I thought the final result of a library of student-created video lessons on each topic for the semester was pretty cool.

Things to change/remember for next time:

• Show students the process of uploading/TITLING a video in FlipGrid! I kind of forgot that these students might not have used FlipGrid before, because I’ve used it in all of my other classes.
• Make checkpoints due at 8:15am the next day so they can post them using the school wi-fi.
• Grading took FOREVER – maybe have them make the videos with a partner?

Some student comments…

Fun with Quadratics (Desmos Activities)

We’ve been working with quadratics in Algebra 2. With our full SEVEN day Thanksgiving break (thanks, snowstorm), it was a bit rough to get back into the swing of things. To get going again, we did a Desmos Sort where students had to take twelve quadratics equations and determine which of the four methods we’ve discussed would be the best choice. This led to some good discussion between students about which method to use.

We are also getting ready to discuss graphs of quadratics, so we ran through the Polygraph for quadratics. I always feel like I underutilize the Polygraph tool, so it was nice to mix it up. I had them play a couple of rounds before we discussed any vocabulary. They were struggling to describe concave up vs. concave down without the appropriate words. “How would you say it looks like…?” Then we paused for discussion and I pulled up a set of sketches I’d made that would require us to use vocab. words, & had them fill in. Then we resumed and they practiced their new words. It was great to compare their questions in earlier rounds to later rounds.

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We followed this up with Polygraph: Parabolas, Part 2, which was great for additional practice.